8 Answers
8

The aperture affects not only the amount of time required to take a photo, but also the depth of field within it.

With a wide aperture (so a low number, like f/1.8) gives a shallow depth of field - sometimes less than a millimetre with a macro lens. Because a lot of light is reaching the sensor (be it film or digital), this allows for fast shutter speeds

With a narrow aperture (so a high number like f/22), the depth of field is much greater, which is useful for things like landscape photography - it will limit the amount of light reaching your sensor, so you will get slower shutter speeds, which makes a tripod handy.

Aperture simply means "opening", and in photography we use the term to
refer to the diameter of the opening in a special adjustable diaphragm
within each lens. When this diaphragm is constricted, there's less physical
space for light to get in, so naturally the exposure is darker, and a
more-open aperture allows more light and results in a lighter exposure.

Aperture has another important property. When the aperture is very small,
the admitted light is highly "collimated", which is a fancy way of saying
"all the rays are nicely parallel to each other". This results in a sharp
focus for all the light that comes in. When the aperture is more open, only
the rays which closely match the focus point are collimated — which
means that whatever you've focused on is sharp, but farther or closer parts
of the scene will be increasingly blurry.

Lens aperture is usually given as an f-number, which is a ratio of the
focal length of the lens to the effective size of the aperture. This is more
convenient than using physical diameter, because it works out that the
actual amount of light gathered for a given physical aperture size depends
on the focal length — so, if one uses the ratios, the exposure is the
same regardless of lens length. (The counter-intuitive side-effect of this
scheme is that smaller f-numbers let in more light.)

These f-numbers are used in photography in a sequence which may seem
irrational: f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, and so on.
However, these are chosen for a simple reason: each one has twice the area
of the previous, letting in twice as much light. (There's no mystery to the
numbers — the area of a circle is π × radius squared, and you
can quickly work out that to double the area, one must simply increase the
diameter by a factor of √2.)

Each step in the sequence is called "one stop", presumably because on manual
lenses there's a physical catch which makes the dial which controls aperture
nicely stop at each of these pre-defined points. However, the term "one
stop" is generally also used by analogy for shutter speed and sensor ISO
to mean "the amount by which this factor must be adjusted to double or half
the recorded exposure".

An important thing to keep in mind is that while a small aperture excludes
non-parallel light rays, as the size of the aperture approaches the
wavelength of the light being captured, another effect comes into play:
diffraction, which is a bending and scattering of waves as they pass through
the aperture. In practical terms, this begins to affect APS-C form-factor
cameras at around f/8, and so stopping down much beyond may increase depth of field at the expense of decreased sharpness in the in-focus areas. At some point, the effect of diffaction becomes strong enough that stopping down the aperture further doesn't provide any benefit at all.

Aperture is how much light can come into your lens (like an iris on your eye). Assuming two lenses have the same size opening, a wider aperture value (smaller f stop #) will let more light in than the same size lens with a larger minimum aperture value.

A wide aperture will need a shorter shutter speed, which means you can capture high speed motion quicker. More light means a lower ISO setting is needed, which means less grainyness in low light. A wider aperture will allow you to take photos in lower levels of light.

A wide aperture will result in a shallower depth of focus (the in focus part of the image will be smaller in the direction directly outward from the camera)

The aperture of a lens is the opening in the diaphragm that controls how much light is allowed to reach your focal plane (film or sensor). The aperture is usually rated as a fraction of the focal length, hence the f/x.y nomenclature. The wider an aperture is, the more light it allows through, and the smaller the number under f/ is. A common wide aperture is f/2.8, and is called a "fast" lens. A common tight aperture is f/5.6, and is called a "slow" lens. Tighter apertures allow less light through, which requires an decrease in shutter speed to maintain the same exposure.

For a much more detail answer about aperture, including the basic mathematics behind how they affect light, you can see my reply to this question:

Aperture is often confused and considered backwards - larger hole, smaller number - but this isn't really the case. Aperture is measured in a ratio, so its really a ratio of the diameter of the aperture in comparison to the focal length of the lens. This is why it seems backwards, because a smaller number in the denominator is really a larger number (e.g. 1/ 2.8 > 1/5.6). As said in other answers, the size of the aperture affects the amount of light let in, so changing it forces you to compensate with shutter speed and/or ISO and/or ambient light changes.

I find this explanation rather confusing for the following reasons: Aperture is often confused and considered backwards… What follows is generally true: larger hole, smaller number (number being the f/ focal ratio). Then, you say, "But… and go on. The next statement that Aperture is measured in a ratio, so… Aperture is "expressed" as a ratio… is what I was looking for here. What's my point? The OP and the editor have so much experience and intuitively know the subject so well, they have lost the ability to see how confusing this can be for one who doesn't really know. I mean this with respect.
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StanSep 4 '13 at 22:54

One thing to consider is that although some lenses do have low apertures, there can be aberrations at the lower f numbers, this is due to the lenses not being perfect so to get the best sharpness across an image a more midle range aperture may be ideal as it cuts out light that has passed through the slightly off perfection glass of the centre of the lens. It does it does depend on your subject if this matters to you.

Aperture is how open your lens is (lack of a better phrase). The lower the number, the more light you allow in, but the less depth of field. The higher the number, the more depth of field and the less light being let in. Example: Taking a shot of something up close might need a lower aperture to capture ONLY that item, person, etc, and leave the background out of focus, while leaving the subject well lit (depending on your other settings). While a larger shot, might require a higher aperture, in order to keep everything in focus.

Started typing this answer out to the other question before it was marked as a duplicate of this one.

Is there such a thing as a maximum aperture that a lens can be open to?

Yes, it's contained in the name and marketing materials of, and is one of the most prominent markings on, any camera lens.

If you're asking about lens design in general, the maximum aperture is limited by the size and weight of its lens elements and of certain limitations of the lens design. Also, with bigger, heavier elements and a larger lens body comes greater cost.

What about a minimum aperture that it can be closed to?

This is a less important specification and is not usually provided everywhere the maximum aperture is provided. Unlike the maximum aperture, there is rarely a good reason to use a minimum aperture of any lens. It would be normal to assume that the minimum aperture of a DSLR lens is going to be f/22 or smaller, and yet it would be rare to have a reason to go smaller than, say, f/11.

When you use smaller apertures there is a point at which the diffraction from the aperture blades start to make the image blurrier than any benefit that the small aperture has.

Is there a lens with the narrowest aperture in the world?

Again, it's not a very important statistic so there's no real reason to strive to it.

However, you may be interested in looking into what a pinhole camera is. It is a camera which has a tiny opening for light to pass through. Effectively it is an aperture so small that no lens is needed to focus the light.

Is there one with the widest?

Lenses get bigger, heavier and more expensive with increasing aperture. There are physical limits to maximum aperture. Lenses with a f/0.95 maximum aperture do exist, which means that the effective aperture diameter is a little larger than the focal distance.